Projection-free approximation of geometrically constrained partial differential equations
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Abstract:
We devise algorithms for the numerical approximation of partial differential equations involving a nonlinear, pointwise holonomic constraint. The elliptic, parabolic, and hyperbolic model equations are replaced by sequences of linear problems with a linear constraint. Stability and convergence hold unconditionally with respect to step sizes and triangulations. In the stationary situation a multilevel strategy is proposed that iteratively decreases the step size. Numerical experiments illustrate the accuracy of the approach.References
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Additional Information
- Sören Bartels
- Affiliation: Department of Applied Mathematics, Mathematical Institute, University of Freiburg, Hermann-Herder-Str 9, 79104 Freiburg i. Br., Germany
- Email: bartels@mathematik.uni-freiburg.de
- Received by editor(s): August 20, 2013
- Received by editor(s) in revised form: April 7, 2014, and October 21, 2014
- Published electronically: July 21, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 1033-1049
- MSC (2010): Primary 65N12; Secondary 65N15, 65N30
- DOI: https://doi.org/10.1090/mcom/3008
- MathSciNet review: 3454357